8.16: Exercise- Using the Averaged HEOG to Visualize Consistent Eye Movements
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In an N2pc (or CDA or LRP) experiment, we’re mainly concerned about systematic eye movements in the direction of the target, not random eye movements. A good way to assess these systematic eye movements is to make one averaged HEOG waveform for all the left-target trials and another averaged waveform for all the right-target trials. That’s what we’ll do in this exercise, before we work on rejecting trials with artifacts.
To begin the exercise, make sure that 15_N2pc_ICA_preprocessed is still loaded and active. Select EEGLAB > ERPLAB > Compute averaged ERPs , and run it with the default settings. You can name the resulting ERPset 15_N2pc_no_rejection . Select EEGLAB > ERPLAB > Plot ERPs > Plot ERP waveforms to plot the data, but telling the routine to plot only Channel 32 (HEOG-bipolar). It should look something like Screenshot 8.7.A.
Starting just after 200 ms, you can see a positive voltage deviation (leftward eye movement) for the left-target trials and a negative voltage deviation (rightward eye movement) for the right-target trials. (There are also small differences between left- and right-target trials at earlier latencies, but they must be random noise because it takes at least 150 ms for the visual system to find a color-defined target in a visual search array and execute a saccade to it.)
The negative voltage in the right-target average is larger than the positive voltage for the left-target average. This is a fairly common pattern, and it may be related to the widely observed right hemifield bias for spatial attention. The main issue, however, is the overall difference in HEOG activity between left-target trials and right-target trials. To visualize this, we can make a left-target-minus-right-target difference wave. Select EEGLAB > ERPLAB > ERP Operations > ERP Bin Operations, and create an equation that reads bin3 = bin1 - bin2 label Left Target Minus Right Target . Make sure that the Mode is set to Modify existing ERPset , and then click RUN .
If you plot the resulting difference wave, you’ll see that the difference between the left- and right-target averages is approximately 8 µV between approximately 250 and 450 ms (see Screenshot 8.7B). However, keep in mind that this reflects a mixture of some trials with a large eye movement and some trials without.
Is this a large enough difference to be problematic? To answer this question, we need to think about why horizontal eye movements are problematic for interpreting an N2pc experiment (or a CDA experiment, LRP experiment, etc.). First, we need to ask whether our N2pc effect might actually be HEOG voltage that has propagated from the eyes to the posterior electrodes where the N2pc is ordinarily observed. Fortunately, a great paper by Lins et al. (1993) provides propagation factors for blinks, vertical eye movements, and horizontal eye movements. They don’t provide values for the PO7 and PO8 electrodes, but they do provide values for the O1 and O2 electrodes and the P5 and P6 electrodes. The PO7 and PO8 electrodes that we used to measure N2pc amplitude in the ERP CORE paper are halfway between O1/P5 and O2/P6. Lins et al. reported a propagation of 1% from HEOG-bipolar to O1 and O2 and a propagation of 3% from HEOG-bipolar to P5 and P6. If we split the difference and assume a 2% propagation to PO7 and PO8, the 8 µV voltage deflection we observed at the HEOG channel in this participant would be expected to lead to a voltage of 0.16 µV at P5 and P6. That’s quite a bit smaller than the N2pc, which is typically 1-2 µV, but still as big as some between-condition differences in N2pc amplitude. And in many participants, the HEOG-bipolar voltage would be quite a bit larger.
We also need to consider whether the eye movements caused the target to shift toward the center of the retina, reducing the lateralization that is necessary for seeing an N2pc (because it is defined by the difference between contralateral and ipsilateral channels). Again, the paper by Lins et al. (1993) provides useful information. Specifically, they found that the HEOG-bipolar signal increases by 16 µV for every degree of lateral eye rotation (which my lab has confirmed several times). Because the difference between left-target and right-target trials in the average HEOG-bipolar signal was approximately 8 µV, we can conclude that there was a 0.5° difference in eye rotation between left-target and right-target trials, on average. However, this is just an average. It’s quite plausible that the target was fully foveated by ~250 ms on a substantial proportion of trials, with little or no eye movement on other trials. On the subset of trials with large eye movements, we can’t be certain that a target on the left side of the video display was actually in the left visual field and that a target on the right side of the video display was actually in the right visual field.
If we want to be careful, we need to both decrease the artifactual EOG voltage produced by the eye movements and eliminate trials with large deviations in eye position. Artifact correction can be used to reduce the artifactual EOG voltage (as described in the next chapter), but we need to reject trials with large eye movements to deal with large deviations in eye position.


12.14: To Index or Not to Index?
Learning Outcomes
- Determine when to use an index
Despite the stated advantages of indexing, there are some drawbacks as well. Indexes add metadata to the database, which increases its size and disk space requirements. In addition, when a new record is added to an indexed table, there is a slight performance hit—for 20 indexes on a table, Access will make 20 adjustments when a new record is added or subtracted. So, you will want to avoid indexing on smaller tables or tables that are not frequently involved in queries.
Contributors and Attributions
CC licensed content, Original
- To Index or Not to Index?. Authored by : Robert Danielson. Provided by : Lumen Learning. License : CC BY: Attribution


6.9: Music of Johannes Brahms (1833-1897)
Whereas Berlioz’s program symphony might be heard as a radical departure from earlier symphonies, the music of Johannes Brahms is often thought of as breathing new life into classical forms. For centuries, musical performances were of compositions by composers who were still alive and working. In the nineteenth century that trend changed. By the time that Johannes Brahms was twenty, over half of all music performed in concerts was by composers who were no longer living; by the time that he was forty, that amount increased to over two-thirds. Brahms knew and loved the music of forebears such as Bach, Handel, Haydn, Mozart, Beethoven, Schubert, and Schumann. He wrote in the genres they had developed, including symphonies, concertos, string quartets, sonatas, and songs. To these traditional genres and forms, he brought sweeping nineteenth-century melodies, much more chromatic harmonies, and the forces of the modern symphony orchestra. He did not, however, compose symphonic poems or program music as did Hector Berlioz and Franz Liszt.
Brahms himself was keenly aware of walking in Beethoven’s shadow. In the early 1870s, he wrote to conductor friend Hermann Levi, “I shall never compose a symphony.”  Nevertheless, some six years later, after a twenty-year period of germination, he premiered his first symphony. Brahms’s music engages Romantic lyricism, rich chromaticism, thick orchestration, and rhythmic dislocation in a way that clearly goes beyond what Beethoven had done. Still, his intensely motivic and organic style, and his use of a four movement symphonic model that features sonata, variations, and ABA forms is indebted to Beethoven.
The third movement of Brahms’s First Symphony is a case in point. It follows the ABA form, as had most moderate-tempo, dance-like third movements since the minuets of the eighteenth-century symphonies and scherzos of the early nineteenth-century symphonies. This movement uses more instruments and grants more solos to the woodwind instruments than earlier symphonies did (listen especially for the clarinet solos). The musical texture is thicker as well, even though the melody always soars above the other instruments. Finally, this movement is more graceful and songlike than any minuet or scherzo that preceded it. In this regard, it is more like the lyrical character pieces of Chopin, Mendelssohn, and the Schumanns than like most movements of Beethoven’s symphonies. But, it does not have an extra musical referent; in fact, Brahms’ music is often called “absolute” music, that is, music for the sake of music. The music might call to a listener’s mind any number of pictures or ideas, but they are of the listener’s imagination, from the listener’s interpretation of the melodies, harmonies, rhythms, and textures written by Brahms. In this way, such a movement is very different than a movement from a program symphony such as Berlioz’s Symphonie fantastique . Public opinion has often split over program music and absolute music. What do you think? Do you prefer a composition in which the musical and extra musical are explicitly linked, or would you rather make up your own interpretation of the music, without guidance from a title or story?
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Listening Guide For audio, go to: https://www.youtube.com/watch?v=dekswN0JqCs Performed by the Berlin Philharmonic Herbert von Karajan conducting |
| Composer: Johannes Brahms |
| Composition: Symphony No. 1 in C minor, Op. 68, III. Un poco allegretto e grazioso [a little allegretto and graceful] |
| Date: 1876 |
| Genre: Symphony |
| Form: ABA moderate-tempoed, dancelike movement from a symphony |
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Performing Forces: Romantic symphony orchestra, including two flutes, two oboes, two clarinets, two bassoons, one contrabassoon, four horns, two trum- pets, three trombones, timpani, violins (first and second), violas, cellos, and double basses |
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What we want you to remember about this composition:
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Other things to listen for: •The winds as well as the strings get the melodic themes from the beginning |
| Timing | Performing Forces, Melody, and Texture | Text and Form |
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0:00 |
Clarinet solo with descending ques- tion phrases answer phrase in the flutes.
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A |
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1:01 |
Second theme: starts with a clarinet solo and then with the whole wood- wind section.
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| 1:26 | Return of opening theme (clarinet solo) |
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1:41 |
New theme introduced and repeated by different groups in the orchestra.
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B |
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3:17 |
First theme returns answer theme in the strings (varied form). Sparser accompaniment again Softer dynamic |
’A’ |
| 3:32 | Second theme: This time it is extended using sequences | |
| 4:00 | Ascending sequential treatment of Coda motives from the movement | Coda |
As noted at the beginning of this chapter, political and cultural nationalism strongly influenced many creative works of the nineteenth century. We have already observed aspects of nationalism in the piano music of Chopin and Liszt. Later nineteenth-century composers invested even more heavily in nationalist themes.


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antihistamines
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drugs used to treat symptoms of allergies
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antitussives
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drugs used to relieve nonproductive coughs
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cystic fibrosis
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a genetic condition that causes mucus to be sticky and thick, leading to blockages, damage, and infections
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decongestants
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drugs used to relieve nasal congestion caused by respiratory disorders
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expectorants
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drugs that help to clear mucus from the airway
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histamines
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chemicals in body cells that are responsible for many of the symptoms of allergies
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Mallory-Weis tears
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lacerations in the esophagus or stomach that occur from prolonged vomiting or coughing; often seen in clients with alcohol misuse
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methamphetamine
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a potent central nervous system stimulant mainly used as a recreational drug
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monoamine oxidase inhibitors (MAOIs)
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a class of drugs often used to treat depression and panic disorder
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mucolytics
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drugs that help to clear mucus from the upper and lower airways of the respiratory system
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muscarinic
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a type of receptor in the body that mediates parasympathetic effects such as slow heart rate and increased activity of smooth muscle tissue
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rebound congestion
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constant nasal congestion resulting from overuse of nasal decongestants
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urticaria
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raised itchy rash that appears on the skin


14.3.2: Managed Care Organizations
Managed Care Organizations (MCOs) include both Preferred Provider Organizations (PPOs) and Health Management Organizations (HMOs). MCOs make up the majority of health insurance plans in the marketplace today, including those offered by employers and on state or national marketplaces created by the Affordable Care Act (ACA). Doctors and other healthcare providers are paid in different ways, either through capitation (a per-member-per-month fee) or through established amounts for similar services (often called prospective reimbursement). Some organizations contract with a provider organization which pays doctors and other healthcare providers salaries, eliminating the need for doctors to be involved with costs at all. These methods reduce the incentives for doctors to perform unnecessary medical procedures or tests, and helps prevent premiums from rising uncontrollably. The primary difference between a PPO and an HMO is the choice of doctors. A PPO typically has contracts with providers (or provider organizations), and those “in-network” providers are covered by the insurance plan at a specific percentage. A PPO patient can go see another doctor, but an “out-of-network” doctor visit would be covered at a lower percentage. For example, an 80/60 plan would cover 80% of the cost of an in-network provider, but only 60% of the cost of an out-of-network provider. An HMO on the other hand, only covers specific providers, and requires a referral from a primary care physician for someone to see a specialist (Shi & Singh, 2017)


9.15: Discusión. Discussion- ¿Qué hábitos tienes?
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- Romano Sánchez Domínguez
- Imperial Valley College
Purpose : You will practice your conversation skills in Spanish by listening to a recording and responding to the questions about your life and habits in Spanish, as well as asking questions to your fellow classmates. You will get exposure to different stem-changing and irregular verbs in the questions, and you will respond to these questions in the yo form, changing the verbs as necessary. Hint: many of these are “yo-go” verbs.
Task : This activity has four parts.
- An initial listening activity
- An audio recording based on the prompts in the listening portion
- A written response in Spanish to two peers’ questions
- A final written response in Spanish to peers’ follow up questions
Part 1 . Listen to the following questions about your life and habits in Spanish. You may read along with the Spanish instructor. Notice the spelling and pronunciation of the stem-changing verbs presented in this activity.
- ¿Tienes tarea todos los días? ¿Dónde haces las tareas para tus clases?
- ¿Haces deportes? ¿Qué días?
- ¿Pones atención en clase a las explicaciones de tus profesores? ¿Cuál clase es más difícil para ti?
- ¿Traes los libros contigo (with you) en tu mochila todos los días?
- ¿Sales con tus amigos los fines de semana? ¿Adónde van?
- ¿Dices la verdad siempre? O ¿a veces dices mentiras? ¿Cuándo? ¿A quién?
- ¿Ves “youtube” todos los días? ¿Qué ves en “youtube”?
- ¿Oyes conversaciones ajenas (Do you eavesdrop/hear other people’s conversations) a veces? ¿Cuándo? ¿De quién?
- ¿Das dinero a los pobres necesitados (in need)? ¿Cuándo? ¿A quiénes?
Part 2 . Pick three questions you want to answer and three questions you want to ask your fellow classmates (these may be the same or different, but they need to be from the 9 questions presented in the original audio file by the Spanish instructor). Using a computer or a voice memo function on a smartphone, in a single audio file record your answers to the 3 questions you selected to answer in Spanish, along with the 3 questions you chose to ask you peers (if you make mistakes, it is okay and expected; start over from the beginning of the sentence and keep recording). Post the audio file including your three responses and three questions in Spanish to the discussion board. Others will be able to hear your responses and questions in Spanish, just as you can hear theirs.
Part 3 . You will respond to the original posts of two classmates by answering the three questions they asked you and asking them one question in return. This question must be a complete question from the original 9 presented; it cannot be ¿y tú? for this activity.
Part 4 . Just as you have responded to the three questions of two of your peers and asked them an additional question, some of your peers have responded to your questions and asked you a question on your original post. Finish up the conversations by responding to each peer who commented on your original post. Answer their questions, and politely thank them for their time and sign off.
Criteria: The components of this activity add up to 100%.
Parts 1 & 2. 30% of the grade for this activity is earned in this portion of the activity. You will hear 9 questions, and you will choose 3 questions that you would like to answer and 3 questions you would like to pose to your classmates. Record your 3 responses plus your 3 questions in Spanish in a single audio file (if you make mistakes, it is okay and expected; start over from the beginning of the sentence and keep recording). Each response is worth 5% and each question for your peers is worth 5%.
Part 3. 40% of your grade will be earned for interacting with two peers on their initial posts: you are to answer the three questions on the posts of two peers, so each answer is worth 5% and responding with one follow up question per peer is worth 5%.
Part 4. 30% of your grade will be earned for responding to your peers on your original post: you are to use Spanish to answer the follow up question that your two peers asked on your original post (10% each) and politely thank them and sign off (5% each).
Ejemplo :
Rashon listens to the recording. He then chooses which three questions he wants to answer and which three he wants to ask to his classmates. Rashon then records his responses in Spanish to the three questions he chooses to answer and he ends by asking three questions in Spanish to his classmates. He uploads this single audio file to the discussion board. He has earned 30% of the points for this activity.
Rashon then finds two peers, Elie and Rebecca, and he listens to their responses to the original prompt, as well as the follow up questions they ask him. He then prepares his responses, paying careful attention to the changes to the verbs and being sure to answer each question completely. He writes his answers to each of his peers’ three questions, and he follows up with one additional question that was on the Spanish instructor’s recording. He has earned 40% of the points for this activity.
Rashon goes back to his original post and sees that two of his classmates have answered the questions he asked. He reads their responses and their follow up questions carefully. He writes a final message for each peer in which he answers their follow up question, thanks them by name, and signs off.
- Script
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In this activity, you will hear a series of questions to elicit conversation using irregular and stem-changing verbs. There are nine conversation points, and each conversation point will have additional follow up questions. A new conversation point will be introduced by a number. Feel free to pause the recording as necessary and to take notes about what you hear so that you can prepare a response.
1. ¿Tienes tarea todos los días? ¿Dónde haces las tareas para tus clases?
2. ¿Haces deportes? ¿Qué días?
3. ¿Pones atención en clase a las explicaciones de tus profesores? ¿Cuál clase es más difícil para ti?
4. ¿Traes los libros contigo (with you) en tu mochila todos los días?
5. ¿Sales con tus amigos los fines de semana? ¿Adónde van?
6. ¿Dices la verdad siempre? O ¿a veces dices mentiras? ¿Cuándo? ¿A quién?
7. ¿Ves “youtube” todos los días? ¿Qué ves en “youtube”?
8. ¿Oyes conversaciones ajenas (Do you eavesdrop/hear other people’s conversations) a veces? ¿Cuándo? ¿De quién?
9. ¿Das dinero a los pobres necesitados? ¿Cuándo? ¿A quiénes?
Contributors and Attributions
- Discussion: Que habitos tienes. Authored by : Diamond Wilson with Lumen Learning. License : CC BY: Attribution


2.8: Review- Hardware Jeopardy
A Jeopardy game is attached to assist you in your review. You will need the PowerPoint application or a PowerPoint viewer to play the game. You can perform these exercises on your mobile devices with access to Office 365 Mobile or a separate App for your Apple or Android device.
Jeopardy: Hardware Review
NOTE: The Jeopardy Game should open in the Slide Show view and be immediately playable. If it opens in the regular PowerPoint presentation view, go to the SLIDE SHOW tab on the ribbon and start the show from THE BEGINNING (command on the far left). You can play the game as many times as you like and in any order you like.
- Introduction to Computer Applications and Concepts, Module 2. Authored by : Jim Shannon. Provided by : Extended Learning Institute of Northern Virginia Community College. Located at : http://www.nvcc.edu/eli/index.html . License : CC BY: Attribution


13.9.5: Simplify Complex Rational Expressions
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Learning Objectives
By the end of this section, you will be able to:
- Simplify a complex rational expression by writing it as division
- Simplify a complex rational expression by using the LCD
Note
Before you get started, take this readiness quiz.
If you miss a problem, go back to the section listed and review the material.
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Simplify: \(\frac{\frac{3}{5}}{\frac{9}{10}}\).
If you missed this problem, review Exercise 1.6.25 . -
Simplify: \(\frac{1−\frac{1}{3}}{4^2+4·5}\).
If you missed this problem, review Exercise 1.6.31 .
Complex fractions are fractions in which the numerator or denominator contains a fraction. In Chapter 1 we simplified complex fractions like these:
\[\begin{array}{cc} {\frac{\frac{3}{4}}{\frac{5}{8}}}&{\frac{\frac{x}{2}}{\frac{xy}{6}}}\\ \nonumber \end{array}\]
In this section we will simplify complex rational expressions , which are rational expressions with rational expressions in the numerator or denominator.
Definition: COMPLEX RATIONAL EXPRESSION
A complex rational expression is a rational expression in which the numerator or denominator contains a rational expression.
Here are a few complex rational expressions:
\(\frac{\frac{4}{y−3}}{\frac{8}{y^2−9}}\)
\(\frac{\frac{1}{x}+\frac{1}{y}}{\frac{x}{y}−\frac{y}{x}}\)
\(\frac{\frac{2}{x+6}}{\frac{4}{x−6}−\frac{4}{x^2−36}}\)
Remember, we always exclude values that would make any denominator zero.
We will use two methods to simplify complex rational expressions.
Simplify a Complex Rational Expression by Writing it as Division
We have already seen this complex rational expression earlier in this chapter.
\(\frac{\frac{6x^2−7x+2}{4x−8}}{\frac{2x^2−8x+3}{x^2−5x+6}}\)
We noted that fraction bars tell us to divide, so rewrote it as the division problem
\((\frac{6x^2−7x+2}{4x−8})÷(\frac{2x^2−8x+3}{x^2−5x+6})\)
Then we multiplied the first rational expression by the reciprocal of the second, just like we do when we divide two fractions.
This is one method to simplify rational expressions. We write it as if we were dividing two fractions.
Example \(\PageIndex{1}\)
\(\frac{\frac{4}{y−3}}{\frac{8}{y^2−9}}\).
- Answer
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\(\frac{\frac{4}{y−3}}{\frac{8}{y^2−9}}\) Rewrite the complex fraction as division. \(\frac{4}{y−3}÷\frac{8}{y^2−9}\) Rewrite as the product of first times the reciprocal of the second. \(\frac{4}{y−3}·\frac{y^2−9}{8}\) Multiply. \(\frac{4(y^2−9)}{8(y−3)}\) Factor to look for common factors. \(\frac{4(y−3)(y+3)}{8(y−3)}\) Simplify. \(\frac{y+3}{2}\) Are there any value(s) of y that should not be allowed? The simplified rational expression has just a constant in the denominator. But the original complex rational expression had denominators of y−3 and \(y^2−9\). This expression would be undefined if y=3 or y=−3
Example \(\PageIndex{2}\)
\(\frac{\frac{2}{x^2−1}}{\frac{3}{x+1}}\).
- Answer
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\(\frac{2}{3(x−1)}\)
Example \(\PageIndex{3}\)
\(\frac{\frac{1}{x^2−7x+12}}{\frac{2}{x−4}}\).
- Answer
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\(\frac{1}{2(x−3)}\)
Example \(\PageIndex{4}\)
\(\frac{\frac{1}{3}+\frac{1}{6}}{\frac{1}{2}−\frac{1}{3}}\).
- Answer
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Simplify the numerator and denominator. Find the LCD and add the fractions in the numerator.
Find the LCD and add the fractions in the denominator.Simplify the numerator and denominator. Simplify the numerator and denominator, again. Rewrite the complex rational expression as a division problem. Multiply the first times by the reciprocal of the second. Simplify.
Example \(\PageIndex{5}\)
\(\frac{\frac{1}{2}+\frac{2}{3}}{\frac{5}{6}+\frac{1}{12}}\).
- Answer
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\(\frac{14}{11}\)
Example \(\PageIndex{6}\)
\(\frac{\frac{3}{4}−\frac{1}{3}}{\frac{1}{8}+\frac{5}{6}}\).
- Answer
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\(\frac{10}{23}\)
How to Simplify a Complex Rational Expression by Writing it as Division
Example \(\PageIndex{7}\)
\(\frac{\frac{1}{x}+\frac{1}{y}}{\frac{x}{y}−\frac{y}{x}}\).
- Answer
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Example \(\PageIndex{8}\)
\(\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x}−\frac{1}{y}}\).
- Answer
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\(\frac{y+x}{y−x}\)
Example \(\PageIndex{9}\)
\(\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a^2}−\frac{1}{b^2}}\).
- Answer
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\(\frac{ab}{b−a}\)
Definition: SIMPLIFY A COMPLEX RATIONAL EXPRESSION BY WRITING IT AS DIVISION.
- Simplify the numerator and denominator.
- Rewrite the complex rational expression as a division problem.
- Divide the expressions.
Example \(\PageIndex{10}\)
\(\frac{n−\frac{4n}{n+5}}{\frac{1}{n+5}+\frac{1}{n−5}}\)
- Answer
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Simplify the numerator and denominator. Find the LCD and add the fractions in the numerator.
Find the LCD and add the fractions in the denominator.Simplify the numerators.
Subtract the rational expressions in the numerator and add in the denominator.Rewrite as fraction division. Multiply the first times the reciprocal of the second. Factor any expressions if possible. Remove common factors. Simplify.
Example \(\PageIndex{11}\)
\(\frac{b−\frac{3b}{b+5}}{\frac{2}{b+5}+\frac{1}{b−5}}\).
- Answer
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b(b+2)
Example \(\PageIndex{12}\)
\(\frac{1−\frac{3}{c+4}}{\frac{1}{c+4}+\frac{c}{3}}\).
- Answer
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3c+3
Simplify a Complex Rational Expression by Using the LCD
We “cleared” the fractions by multiplying by the LCD when we solved equations with fractions. We can use that strategy here to simplify complex rational expressions. We will multiply the numerator and denominator by LCD of all the rational expressions.
Let’s look at the complex rational expression we simplified one way in Example . We will simplify it here by multiplying the numerator and denominator by the LCD. When we multiply by \(\frac{LCD}{LCD}\) we are multiplying by 1, so the value stays the same.
Example \(\PageIndex{13}\)
Simplify: \(\frac{\frac{1}{3}+\frac{1}{6}}{\frac{1}{2}−\frac{1}{3}}\).
- Answer
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The LCD of all the fractions in the whole expression is 6. Clear the fractions by multiplying the numerator and denominator by that LCD. Distribute. Simplify.
Example \(\PageIndex{14}\)
Simplify: \(\frac{\frac{1}{2}+\frac{1}{5}}{\frac{1}{10}+\frac{1}{5}}\).
- Answer
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\(\frac{7}{3}\)
Example \(\PageIndex{15}\)
Simplify: \(\frac{\frac{1}{4}+\frac{3}{8}}{\frac{1}{2}−\frac{5}{16}}\).
- Answer
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\(\frac{7}{3}\)
How to Simplify a Complex Rational Expression by Using the LCD
Example \(\PageIndex{16}\)
Simplify: \(\frac{\frac{1}{x}+\frac{1}{y}}{\frac{x}{y}−\frac{y}{x}}\).
- Answer
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Example \(\PageIndex{17}\)
Simplify: \(\frac{\frac{1}{a}+\frac{1}{b}}{\frac{a}{b}−\frac{b}{a}}\).
- Answer
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\(\frac{b+a}{a^2+b^2}\)
Example \(\PageIndex{18}\)
Simplify: \(\frac{\frac{1}{x^2}−\frac{1}{y^2}}{\frac{1}{x}−\frac{1}{y}}\).
- Answer
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\(\frac{y−x}{xy}\)
Definition: SIMPLIFY A COMPLEX RATIONAL EXPRESSION BY USING THE LCD.
- Find the LCD of all fractions in the complex rational expression.
- Multiply the numerator and denominator by the LCD.
- Simplify the expression.
Be sure to start by factoring all the denominators so you can find the LCD.
Example \(\PageIndex{19}\)
Simplify: \(\frac{\frac{2}{x+6}}{\frac{4}{x−6}−\frac{4}{x^2−36}}\).
- Answer
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Find the LCD of all fractions in the complex rational expression. The LCD is (x+6)(x−6) Multiply the numerator and denominator by the LCD. Simplify the expression. Distribute in the denominator. Simplify. Simplify. To simplify the denominator, distribute and combine like terms. Remove common factors. Simplify. Notice that there are no more factors common to the numerator and denominator.
Example \(\PageIndex{20}\)
Simplify: \(\frac{\frac{3}{x+2}}{\frac{5}{x−2}−\frac{3}{x^2−4}}\).
- Answer
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\(\frac{3x−6}{5x+7}\)
Example \(\PageIndex{21}\)
Simplify: \(\frac{\frac{2}{x−7}−\frac{1}{x+7}}{\frac{6}{x+7}−\frac{1}{x^2−49}}\).
- Answer
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\(\frac{x+21}{6x+43}\)
Example \(\PageIndex{22}\)
Simplify: \(\frac{\frac{4}{m^2−7m+12}}{\frac{3}{m−3}−\frac{2}{m−4}}\).
- Answer
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Find the LCD of all fractions in the complex rational expression. The LCD is (m−3)(m−4) Multiply the numerator and denominator by the LCD. Simplify. Simplify. Distribute. Combine like terms.
Example \(\PageIndex{23}\)
Simplify: \(\frac{\frac{3}{x^2+7x+10}}{\frac{4}{x+2}+\frac{1}{x+5}}\).
- Answer
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\(\frac{3}{5x+22}\)
Example \(\PageIndex{24}\)
Simplify: \(\frac{\frac{4y}{y+5}+\frac{2}{y+6}}{\frac{3y}{y^2+11y+30}}\).
- Answer
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\(\frac{6y+34}{3y}\)
Example \(\PageIndex{25}\)
Simplify: \(\frac{\frac{y}{y+1}}{1+\frac{1}{y−1}}\).
- Answer
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Find the LCD of all fractions in the complex rational expression. The LCD is (y+1)(y−1) Multiply the numerator and denominator by the LCD. Distribute in the denominator and simplify. Simplify. Simplify the denominator, and leave the numerator factored. Factor the denominator, and remove factors common with the numerator. Simplify.
Example \(\PageIndex{26}\)
Simplify: \(\frac{\frac{x}{x+3}}{1+\frac{1}{x+3}}\).
- Answer
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\(\frac{x}{x+4}\)
Example \(\PageIndex{27}\)
Simplify: \(\frac{1+\frac{1}{x−1}}{\frac{3}{x+1}}\).
- Answer
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\(\frac{x(x+1)}{3(x−1)}\)
Key Concepts
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To Simplify a Rational Expression by Writing it as Division
- Simplify the numerator and denominator.
- Rewrite the complex rational expression as a division problem.
- Divide the expressions.
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To Simplify a Complex Rational Expression by Using the LCD
- Find the LCD of all fractions in the complex rational expression.
- Multiply the numerator and denominator by the LCD.
- Simplify the expression.
Glossary
- complex rational expression
- A complex rational expression is a rational expression in which the numerator or denominator contains a rational expression.


5.1: Dihybrid Crosses
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- Ying Liu
- City College of San Francisco
Mendel’s Second Law
Before Mendel, it had not yet been established that heritable traits were controlled by discrete factors. Therefor an important question was therefore whether distinct traits were controlled by discrete factors that were inherited independently of each other? To answer this, Mendel took two apparently unrelated traits, such as seed shape and seed color, and studied their inheritance together in one individual. He studied two variants of each trait: seed color was either green or yellow, and seed shape was either round or wrinkled. (He studied seven traits in all.) When either of these traits was studied individually, the phenotypes segregated in the classical 3:1 ratio among the progeny of a monohybrid cross (Figure \(\PageIndex{2}\)), with ¾ of the seeds green and ¼ yellow in one cross, and ¾ round and ¼ wrinkled in the other cross. Would this be true when both were in the same individual?
To analyze the segregation of both traits at the same time in the same individual, he crossed a pure breeding line of green, wrinkled peas with a pure breeding line of yellow, round peas to produce F 1 progeny that were all green and round, and which were also dihybrids ; they carried two alleles at each of two loci (Figure \(\PageIndex{3}\)).
If the inheritance of seed color was truly independent of seed shape, then when the F 1 dihybrids were crossed to each other, a 3:1 ratio of one trait should be observed within each phenotypic class of the other trait (Figure \(\PageIndex{3}\)). Using the product law, we would therefore predict that if ¾ of the progeny were green, and ¾ of the progeny were round, then ¾ × ¾ = 9/16 of the progeny would be both round and green (Table \(\PageIndex{1}\)). Likewise, ¾ × ¼ = 3/16 of the progeny would be both round and yellow, and so on. By applying the product rule to all of these combinations of phenotypes, we can predict a 9:3:3:1 phenotypic ratio among the progeny of a dihybrid cross, if certain conditions are met, including the independent segregation of the alleles at each locus. Indeed, 9:3:3:1 is very close to the ratio Mendel observed in his studies of dihybrid crosses, leading him to state his Second Law, the Law of Independent Assortment , which we now express as follows: two loci assort independently of each other during gamete formation.
Definition: Mendel's Second Law
Two loci assort independently of each other during gamete formation.
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Frequency of phenotypic crosses within separate monohybrid crosses: seed shape: ¾ round ¼ wrinkled seed color: ¾ yellow ¼ green Frequency of phenotypic crosses within a dihybrid cross: ¾ round × ¾ yellow = 9/16 round & yellow ¾ round × ¼ green = 3/16 round & green ¼ wrinkled × ¾ yellow = 3/16 wrinkled & yellow ¼ wrinkled × ¼ green = 1/16 wrinkled & green |
The 9:3:3:1 phenotypic ratio that we calculated using the product rule can also be obtained using Punnett Square (Figure \(\PageIndex{4}\)). First, we list the genotypes of the possible gametes along each axis of the Punnett Square. In a diploid with two heterozygous genes of interest, there are up to four combinations of alleles in the gametes of each parent. The gametes from the respective rows and column are then combined in the each cell of the array. When working with two loci, genotypes are written with the symbols for both alleles of one locus, followed by both alleles of the next locus (e.g. AaBb , not ABab ). Note that the order in which the loci are written does not imply anything about the actual position of the loci on the chromosomes.
To calculate the expected phenotypic ratios, we assign a phenotype to each of the 16 genotypes in the Punnett Square, based on our knowledge of the alleles and their dominance relationships. In the case of Mendel’s seeds, any genotype with at least one R allele and one Y allele will be round and yellow; these genotypes are shown in the nine, green-shaded cells in Figure \(\PageIndex{4}\). We can represent all of four of the different genotypes shown in these cells with the notation ( R_Y _), where the blank line (__), means “any allele”. The three offspring that have at least one R allele and are homozygous recessive for y (i.e. R_yy ) will have a round, green phenotype. Conversely the three progeny that are homozygous recessive r , but have at least one Y allele ( rrY_ ) will have wrinkled, yellow seeds. Finally, the rarest phenotypic class of wrinkled, yellow seeds is produced by the doubly homozygous recessive genotype, rryy , which is expected to occur in only one of the sixteen possible offspring represented in the square.
Assumptions of the 9:3:3:1 ratio
Both the product rule and the Punnett Square approaches showed that a 9:3:3:1 phenotypic ratio is expected among the progeny of a dihybrid cross such as Mendel’s RrYy × RrYy . In making these calculations, we assumed that:
- both loci assort independently;
- one allele at each locus is completely dominant; and
- each of four possible phenotypes can be distinguished unambiguously, with no interactions between the two genes that would alter the phenotypes.
Deviations from the 9:3:3:1 phenotypic ratio may indicate that one or more of the above conditions has not been met. Modified ratios in the progeny of a dihybrid cross can therefore reveal useful information about the genes involved.
Linkage is one of the most important reasons for distortion of the ratios expected from independent assortment. Linked genes are located close together on the same chromosome. This close proximity alters the frequency of allele combinations in the gametes. We will return to the concept of linkage in Chapter 7. Deviations from 9:3:3:1 ratios can also be due to interactions between genes. These interactions will be discussed in the remainder of this chapter. For simplicity, we will focus on examples that involve easily scored phenotypes, such as pigmentation. Nevertheless, keep in mind that the analysis of segregation ratios of any markers can provide insight into a wide range of biological processes they represent.


9.1: Elements of Religion
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Following the Al Qaeda attacks on the US on 11 September 2001 (often called 9/11), studies of religion in world politics increased sixfold. In the words of Robert Keohane, the events of 9/11 provoked the realization that ‘worldshaking political movements have so often been fuelled by religious fervour’ (2002, 29). Indeed, whether it is the disruptions of religion-led revolution, the work of religious development agencies responding to natural disasters, peace-making efforts of religious diplomats or a myriad of other examples, even a glance at global affairs over recent decades seems to support the comment of sociologist Peter Berger that ‘the world today … is as furiously religious as it ever was, and in some places more so than ever’ (1999, 2).
Such a view also seems supported by the numbers as ‘worldwide, more than eight-in-ten people identify with a religious group’ (Pew 2012, 9). Are you numbered among the 20 or 80 per cent? Do you think religious influence on global affairs is a welcome inclusion or a significant problem? Regardless of where we stand, it appears a closer look at the ‘religion question’ is in order if we are to establish a fuller picture of IR. The following four elements of religion may provide a useful introduction.
1. God(s) and forces in the public square
The first element of religion is the belief that divine beings and/or forces hold relevance to the meaning and practice of politics today and throughout history. These beings are sometimes understood as a knowable God or gods, sometimes as mythical and symbolic figures from our ancient past and sometimes as impersonal forces beyond the physical realm.
Different religious traditions understand the influence of religion upon politics in different ways. Traditions that we might call ‘fundamental’ propose that politics is a matter of organising society according to divine commands. In Iran, for example, the highest court in the land is a religious one, drawing its principles from the Shia branch of Islam – the second largest Islamic tradition worldwide after the majority Sunni tradition. This court has the power to veto laws of parliament and decide who can hold power. Likewise, in Myanmar (formerly Burma) an influential group of religious monks has started a movement intent on imposing Buddhist principles on the whole country, including non-Buddhist minorities. Thus, some religious politics is based on ‘fundamentals’ that, in the view of adherents, cannot be changed without the standards of society also being compromised.
By contrast, traditions that adopt a ‘contextual’ approach hold that politics is a matter of influencing society according to divine principles but as part of a wider tapestry of influences. For example, religious development organisations such as the Aga Khan Development Network (also from the Shia branch of Islam) work in areas of health care and education in countries of Africa and Asia without seeking to control entire political systems. Likewise, in Myanmar, the so-called Saffron Revolution of 2007 saw Buddhist monks stand with the poor against the ruling military dictatorship and support the beginnings of multi-party democracy. In these examples, religious politics is adapted to changing circumstances and takes into account diverse interests and beliefs across society.
What is common to both fundamental and contextual religious traditions is an understanding that politics is in some sort of interactive relationship with the intentions of, or traditions shaped by, gods (or God) and spiritual forces. This contrasts strongly with secular approaches that demote, and sometimes deny altogether, a role for religion in political affairs.
Do you believe that religion has a role to play in public debates or should it be confined to private spirituality only? From an individual point of view, we could address this question by asking what it would be like to live in societies that are either entirely controlled by religion, or entirely without religion. What would the benefits and losses be in each situation? It can be strongly argued that neither scenario exists in pure form. When religion has been used to dominate the public square, a diversity of groups (non-religious and religious) have risen in opposition. Likewise, when religion has been expelled from the public domain, religious actors and interests go underground waiting for a chance to re-emerge.
2. Sacred symbols (re)defining what is real
The second element of religion are rituals that re-order the world according to religious principle. Although the word ‘faith’ can be associated with belief in unseen realities, humans throughout time have needed to see, touch and smell the sacred. Our senses are portals to the spirit. Therefore, rituals function as tangible symbols of the intangible realm. For examples of different studies that consider the public rituals of Judaism, Islam and Hinduism respectively see Beck (2012), Bronner (2011) and Haider (2011). While some religious rituals are private or hidden, many are performed in public spaces or in ways that are openly accessible to wider society. As such, they are a part of public life – which is one of the original definitions of the word politics.
For religious adherents, rituals symbolise spiritual truths but they can also redefine how power can be understood in the material world. Thomas Merton once described his experience of watching Trappist monks perform the rituals of the Catholic Mass in very political terms. He wrote:
The eloquence of this liturgy [communicated] one, simple, cogent, tremendous truth: this church, the court of the Queen of Heaven, is the real capital of the country in which we are living.  (Merton 1948, 325)
Merton’s experience of redefining power and influence through sacred symbols is true for millions of people practising thousands of different religious rituals each day. Beyond the experience of individuals, states also seek divine blessing. For example, over one-fifth of states today have a monarch (such as a king, queen or emperor). Although monarchs differ in the extent of their powers – from figureheads controlled by parliaments to absolute rulers to variations of these – they all draw their power from some form of religious or spiritual authority. The elaborate rituals of monarchies worldwide are understood by their subjects to symbolise divine blessing for the realm and its citizens, redefining where the real power lies.
3. Sacred stories connecting past, present and future
The third element of religion is teaching traditions based on stories of significant figures, events and ideas from the past and beliefs about the future of time itself – like a spoiler alert about the end of the world. For some religions, however, time itself is an illusion and the main focus is living in the now according to sacred ideas rather than the connection of past–present– future. These elements – interpreting the past, projecting the future, living now – are basic to the development of political ideologies also. Therefore, sometimes religious and political groups can appeal to the same stories or ideas even though the interpretation or intent may differ significantly.
For example, both Jews and Christians uphold the idea of ‘Jubilee’ as central to understanding the story and/or future promise of a Messiah who would usher in a new era of justice with peace (or ‘shalom’). In the 1990s members of both communities appealed to one aspect of Jubilee – a tradition of debt cancellation found in the Hebrew Bible – as the basis for addressing the debt crisis facing developing nations. Only a few years later, this sacred story was used for very different purposes by US president George W. Bush, who celebrated the 2003 invasion of Iraq by quoting a Jubilee text from the Book of Isaiah: ‘To the captives come out, and to those in darkness be free’ (Monbiot 2003). Sacred stories, ideas and teachings from the past have a richness and power that can influence political affairs today and the aspirations we hold for tomorrow. It is no wonder that the anthropologist Talal Asad once observed that what we today call religion has ‘always been involved in the world of power’ (2003, 200).
4. A community worshiping and acting together
The fourth element common to most religions is the need for believers to belong to a faith community in order to practice sacred rituals and reinforce the truth of sacred stories. Some religious traditions could be described as high demand, requiring strict adherence to rules and standards in order to maintain membership of the faith community. Other traditions are low demand, adopting a more flexible approach to the requirements for belonging faithfully to the community. Both forms of faith commitment are expressions of religion as ‘identity politics’ connected to who we are (that is, who we understand ourselves to be) and how we live.
The connection between religion and identity politics can have individual and international significance. For instance, empowered by belonging to a faith community, individuals can act in ways that they might not otherwise have done in isolation. Rosa Parks, an African American woman who famously refused to obey American racial segregation laws and sparked a nation-wide civil rights movement in the 1960s, is often lauded as a heroic individual. This may be true, but as a member of a religious community that affirmed human dignity and the divine principles of racial equality, Rosa Parks was never acting in isolation (Thomas 2005, 230–240). This can be understood internationally also, as many (if not most) faith communities have a transnational membership, and some of these exert significant influence on political issues varying from religion-inspired terrorist action against ‘Western’ values (after all, not all religious politics is peace-orientated) to faith coalitions for environmental sustainability.
The four elements of religion described above – the significance of gods and spirits, the power of holy rituals, the telling of sacred stories and belonging to faith communities – seem in their own ways to be a core aspect of the human condition in the twenty-first century. Although many dimensions of the religious experience can be ‘politics-free’, both history and contemporary events remind us that these combined elements of religion can have a political impact on individuals, nations and international society.


15.2: Suggested Resources
15.1 Launching Your Venture
R. Nanda, L. Kind, K. Laws, & J. Lum. "Case Study: Is a Start-up's Strength Becoming Its Weakness?" Harvard Business Review 93, no. 11 (2015): 145.
Ablebit’s instructions for making a Gantt chart in Microsoft Excel: https://www.ablebits.com/office-addi...t-chart-excel/
Smartsheet’s step-by-step instructions for making a Gantt chart in Microsoft Excel: https://www.smartsheet.com/blog/gantt-chart-excel
Project Manager’s Ultimate Guide to Gantt Charts: https://www.projectmanager.com/gantt-chart
The Startup Checklist by David Rose, founder of NY Angels and GUST.com
Shortcut: How Analogies Reveal Connections, Spark Innovation, and Sell Our Greatest Ideas by John Pollock discusses using analogies to think about unmet needs and innovative solutions.
15.2 Making Difficult Business Decisions in Response to Challenges
“How Fast Can Your Company Afford to Grow?” Harvard Business Review , 1998. Classic article serves as a good reference on cash flow and self-financed growth, covering key levers to help manage profitable growth without having to go “hat in hand” to investors again.
The Undoing Project by Michael Lewis provides a good reference on biases through the story of psychologists Amos Tversky and Daniel Kahneman.
“3 Steps to Determine Product-Market Fit”, Entrepreneur Magazine , August 2014. Good reference on product-market fit.
What Customers Want , by Ullrich, discusses “Jobs to be Done” theory created by Clayton Christensen and practice by Strategyn.
15.3 Seeking Help or Support
Service Corps of Retired Executives (SCORE): https://www.score.org/
Small Business Administration: https://www.sba.gov/
Y Combinator: http://www.ycombinator.com/
Techstars: www.techstars.org
G. Klein. The Power of Intuition: How to Use Your Gut Feelings to Make Better Decisions at Work . (New York: Doubleday, 2004)
15.4 Now What? Serving as a Mentor, Consultant, or Champion
The Case Foundation: https://casefoundation.org/
Startup Champions Network: http://www.championsnetwork.co/
15.5 Reflections: Documenting the Journey
F. T. Evers. Journaling: A Path to Our Innermost Self. Interbeing , 2, no.2 (2008): 53–56.
D. Ciampa.  Harvard Business Review Digital Articles (2017): 2–4.
Worklife TED-sponsored podcasts: https://itunes.apple.com/us/podcast/...346314086?mt=2
NPR podcast “How I Built This” founder/CEO podcasts: https://www.npr.org/podcasts/510313/how-i-built-this


7.2: Models of Classroom Management
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During the mid-1900’s, teachers started to express their concerns about managing classrooms. There was not any systematic approach developed by then. Traditionally, teachers used the authoritative assertion techniques, however, this technique did not last long and began to fade gradually (Allen, 1996). Later, researchers began to observe teachers all over the country to study what worked well and what did not for almost a decade from 1969 to 1979. This led to a systematic development of classroom management models.
There are several models that have been developed over the years. Allen (1996) in his research “Seven Models of Discipline” summarizes seven systematic models of classroom management borrowing from Charles’ book Building Classroom Discipline: From Models to Practice (1985). These models were a derivative of extensive classroom observations studying the student- teacher behavior in addition to considering the psychological aspects of humans (Allen, 1996, p. 1). They are:
Over time scholars built on these models and developed other models based on their classroom needs. Krause, Bochner, & Duchesne (2006) discuss three classroom management models “based on the premise that teachers can diversify their skill set in order to best meet the needs of different groups of students” (as cited in ASCD, 2013).
First, the Noninterventionist model where a teacher helps students meet their potential by “enhancing personal growth building a strong, positive relationship, and assisting students with developing problem-solving abilities” (ASCD, 2013, p. 1). The end goal is to help student reach their potential independent of teacher’s direction.
Second, the Interventionist model where it is believed that students’ development is a “product of environmental conditions brought on by intervention in a student’s daily surroundings” (ASCD, 2013, p. 2). This approach is usually practiced in a positive reinforcement classroom where clear rules and classroom procedures have been established. Further, students are rewarded, or face consequences based on these classroom procedures (ASCD, 2013) The next section on Characteristics of Effective Classroom Management details the keys to successful classroom management and ways to establish a safe learning environment.
Third, the Interactivist model as the name suggests calls for teachers to consider each student’s learning and behavioral needs further helping them understand “their actions and consequences” (ASCD, 2013, p. 2). This approach makes students accountable for their actions and own learning.


12.16: Black Holes and Curved Spacetime (Exercises)
Articles
Black Holes
Charles, P. & Wagner, R. “Black Holes in Binary Stars: Weighing the Evidence.” Sky & Telescope (May 1996): 38. Excellent review of how we find stellar-mass black holes.
Gezari, S. “Star-Shredding Black Holes.” Sky & Telescope (June 2013): 16. When black holes and stars collide.
Jayawardhana, R. “Beyond Black.” Astronomy (June 2002): 28. On finding evidence of the existence of event horizons and thus black holes.
Nadis, S. “Black Holes: Seeing the Unseeable.” Astronomy (April 2007): 26. A brief history of the black hole idea and an introduction to potential new ways to observe them.
Psallis, D. & Sheperd, D. “The Black Hole Test.” Scientific American (September 2015): 74–79. The Event Horizon Telescope (a network of radio telescopes) will test some of the stranger predictions of general relativity for the regions near black holes. The September 2015 issue of Scientific American was devoted to a celebration of the 100th anniversary of the general theory of relativity.
Rees, M. “To the Edge of Space and Time.” Astronomy (July 1998): 48. Good, quick overview.
Talcott, R. “Black Holes in our Backyard.” Astronomy (September 2012): 44. Discussion of different kinds of black holes in the Milky Way and the 19 objects known to be black holes.
Gravitational Waves
Bartusiak, M. “Catch a Gravity Wave.” Astronomy (October 2000): 54.
Gibbs, W. “Ripples in Spacetime.” Scientific American (April 2002): 62.
Haynes, K., & Betz, E. “A Wrinkle in Spacetime Confirms Einstein’s Gravitation.” Astronomy (May 2016): 22. On the direct detection of gravity waves.
Sanders, G., and Beckett, D. “LIGO: An Antenna Tuned to the Songs of Gravity.” Sky & Telescope (October 2000): 41.
Websites
Black Holes
Black Hole Encyclopedia: http://blackholes.stardate.org . From StarDate at the University of Texas McDonald Observatory.
Black Holes: http://science.nasa.gov/astrophysics/focus-areas/black-holes . NASA overview of black holes, along with links to the most recent news and discoveries.
Black Holes FAQ: cfpa.berkeley.edu/Education/BHfaq.html. Frequently asked questions about black holes, answered by Ted Bunn of UC–Berkeley’s Center for Particle Astrophysics.
Black Holes: Gravity’s Relentless Pull: http://hubblesite.org/explore_astronomy/black_holes/home.html . The Hubble Space Telescope’s Journey to a Black Hole and Black Hole Encyclopedia (a good introduction for beginners).
Introduction to Black Holes: www.damtp.cam.ac.uk/research/gr/public/bh_intro.html. The Cambridge University Relativity Group’s pages on black holes and related calculations.
Movies from the Edge of Spacetime: archive.ncsa.illinois.edu/Cyberia/NumRel/MoviesEdge.html. Physicists simulate the behavior of various black holes.
Virtual Trips into Black Holes and Neutron Stars: http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html . By Robert Nemiroff at Michigan Technological University.
Gravitational Waves
Advanced LIGO: www.advancedligo.mit.edu. The full story on this gravitational wave observatory.
eLISA: https://www.elisascience.org .
Gravitational Waves Detected, Confirming Einstein’s Theory: http://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html . New York Times article and videos on the discovery of gravitational waves.
Gravitational Waves Discovered from Colliding Black Holes: http://www.scientificamerican.com/article/gravitational-waves-discovered-from-colliding-black-holes1 . Scientific American coverage of the discovery of gravitational waves (note the additional materials available in the menu at the right).
LIGO Caltech: https://www.ligo.caltech.edu .
Videos
Black Holes
Black Holes: The End of Time or a New Beginning?: https://www.youtube.com/watch?v=mgtJRsdKe6Q . 2012 Silicon Valley Astronomy Lecture by Roger Blandford (1:29:52).
Death by Black Hole: www.openculture.com/2009/02/death_by_black_hole_and_its_kind_of_funny.htm. Neil deGrasse Tyson explains spaghettification with only his hands (5:34).
Hearts of Darkness: Black Holes in Space: https://www.youtube.com/watch?v=4tiAOldypLk . 2010 Silicon Valley Astronomy Lecture by Alex Filippenko (1:56:11).
Gravitational Waves
Journey of a Gravitational Wave: https://www.youtube.com/watch?v=FlDtXIBrAYE . Introduction from LIGO Caltech (2:55).
LIGO’s First Detection of Gravitational Waves: https://www.youtube.com/watch?v=gw-i_VKd6Wo . Explanation and animations from PBS Digital Studio (9:31).
Two Black Holes Merge into One: https://www.youtube.com/watch?v=I_88S8DWbcU . Simulation from LIGO Caltech (0:35).
What the Discovery of Gravitational Waves Means: https://www.youtube.com/watch?v=jMVAgCPYYHY . TED Talk by Allan Adams (10:58).
Review Questions
- If a black hole itself emits no radiation, what evidence do astronomers and physicists today have that the theory of black holes is correct?
- What characteristics must a binary star have to be a good candidate for a black hole? Why is each of these characteristics important?
- A student becomes so excited by the whole idea of black holes that he decides to jump into one. It has a mass 10 times the mass of our Sun. What is the trip like for him? What is it like for the rest of the class, watching from afar?
- What is an event horizon? Does our Sun have an event horizon around it?
- What is a gravitational wave and why was it so hard to detect?
- What are some strong sources of gravitational waves that astronomers hope to detect in the future?
- Suppose the amount of mass in a black hole doubles. Does the event horizon change? If so, how does it change?
Thought Questions
- Imagine that you have built a large room around the people in Figure \(24.1.3\) in Section 24.1 and that this room is falling at exactly the same rate as they are. Galileo showed that if there is no air friction, light and heavy objects that are dropping due to gravity will fall at the same rate. Suppose that this were not true and that instead heavy objects fall faster. Also suppose that the man in Figure \(24.1.3\) in Section 24.1 is twice as massive as the woman. What would happen? Would this violate the equivalence principle?
- A monkey hanging from a tree branch sees a hunter aiming a rifle directly at him. The monkey then sees a flash and knows that the rifle has been fired. Reacting quickly, the monkey lets go of the branch and drops so that the bullet can pass harmlessly over his head. Does this act save the monkey’s life? Why or why not? (Hint: Consider the similarities between this situation and that in the previous exercise .)
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Look elsewhere in this book for necessary data, and indicate what the final stage of evolution—white dwarf, neutron star, or black hole—will be for each of these kinds of stars.
- Spectral type-O main-sequence star
- Spectral type-B main-sequence star
- Spectral type-A main-sequence star
- Spectral type-G main-sequence star
- Spectral type-M main-sequence star
- Which is likely to be more common in our Galaxy: white dwarfs or black holes? Why?
- If the Sun could suddenly collapse to a black hole, how would the period of Earth’s revolution about it differ from what it is now?


12.1.2: The Role of Information Systems
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The Role of Information Systems
Now that we have explored the different components of information systems, we need to turn our attention to the role that information systems play in an organization. So far we have looked at what the components of an information system are, but what do these components actually do for an organization? From our definitions above, we see that these components collect, store, organize, and distribute data throughout the organization. In fact, we might say that one of the roles of information systems is to take data and turn it into information, and then transform that into organizational knowledge. As technology has developed, this role has evolved into the backbone of the organization. To get a full appreciation of the role information systems play, we will review how they have changed over the years.
IBM 704 Mainframe (Copyright: Lawrence Livermore National Laboratory)
The Mainframe Era
From the late 1950s through the 1960s, computers were seen as a way to more efficiently do calculations. These first business computers were room-sized monsters, with several refrigerator-sized machines linked together. The primary work of these devices was to organize and store large volumes of information that were tedious to manage by hand. Only large businesses, universities, and government agencies could afford them, and they took a crew of specialized personnel and specialized facilities to maintain. These devices served dozens to hundreds of users at a time through a process called time-sharing. Typical functions included scientific calculations and accounting, under the broader umbrella of “data processing.”
Registered trademark of International Business Machines
In the late 1960s, the Manufacturing Resources Planning (MRP) systems were introduced. This software, running on a mainframe computer, gave companies the ability to manage the manufacturing process, making it more efficient. From tracking inventory to creating bills of materials to scheduling production, the MRP systems (and later the MRP II systems) gave more businesses a reason to want to integrate computing into their processes. IBM became the dominant mainframe company. Nicknamed “Big Blue,” the company became synonymous with business computing. Continued improvement in software and the availability of cheaper hardware eventually brought mainframe computers (and their little sibling, the minicomputer) into most large businesses.
The PC Revolution
In 1975, the first microcomputer was announced on the cover of Popular Mechanics : the Altair 8800. Its immediate popularity sparked the imagination of entrepreneurs everywhere, and there were quickly dozens of companies making these “personal computers.” Though at first just a niche product for computer hobbyists, improvements in usability and the availability of practical software led to growing sales. The most prominent of these early personal computer makers was a little company known as Apple Computer, headed by Steve Jobs and Steve Wozniak, with the hugely successful “Apple II.” Not wanting to be left out of the revol ution, in 1981 IBM (teaming with a little company called Microsoft for their operating-system software) hurriedly released their own version of the personal computer, simply called the “PC.”  The IBM PC was named Time magazine’s “Man of the Year” for 1982.
Because of the IBM PC’s open architecture, it was easy for other companies to copy, or “clone” it. During the 1980s, many new computer companies sprang up, offering less expensive versions of the PC. This drove prices down and spurred innovation. Microsoft developed itsWindows operating system and made the PC even easier to use. Common uses for the PC during this period included word processing, spreadsheets, and databases. These early PCs were not connected to any sort of network; for the most part they stood alone as islands of innovation within the larger organization.
Client-Server
In the mid-1980s, businesses began to see the need to connect their computers together as a way to collaborate and share resources. This networking architecture was referred to as “client-server” because users would log in to the local area network (LAN) from their PC (the “client”) by connecting to a powerful computer called a “server,” which would then grant them rights to different resources on the network (such as shared file areas and a printer). Software companies began developing applications that allowed multiple users to access the same data at the same time. This evolved into software applications for communicating, with the first real popular use of electronic mail appearing at this time.
This networking and data sharing all stayed within the confines of each business, for the most part. While there was sharing of electronic data between companies, this was a very specialized function. Computers were now seen as tools to collaborate internally, within an organization. In fact, these networks of computers were becoming so powerful that they were replacing many of the functions previously performed by the larger mainframe computers at a fraction of the cost. It was during this era that the first Enterprise Resource Planning (ERP) systems were developed and run on the client-server architecture. An ERP system is a software application with a centralized database that can be used to run a company’s entire business. With separate modules for accounting, finance, inventory, human resources, and many, many more, ERP systems, with Germany’s SAP leading the way, represented the state of the art in information systems integration. We will discuss ERP systems as part of the chapter on process (chapter 9).
The World Wide Web and E-Commerce
First invented in 1969, the Internet was confined to use by universities, government agencies, and researchers for many years. Its rather arcane commands and user applications made it unsuitable for mainstream use in business. One exception to this was the ability to expand electronic mail outside the confines of a single organization. While the first e-mail messages on the Internet were sent in the early 1970s, companies who wanted to expand their LAN-based e-mail started hooking up to the Internet in the 1980s. Companies began connecting their internal networks to the Internet in order to allow communication between their employees and employees at other companies. It was with these early Internet connections that the computer truly began to evolve from a computational device to a communications device.
In 1989, Tim Berners-Lee developed a simpler way for researchers to share information over the network at CERN laboratories, a concept he called the World Wide Web. [4] This invention became the launching point of the growth of the Internet as a way for businesses to share information about themselves. As web browsers and Internet connections became the norm, companies rushed to grab domain names and create websites.
Registered trademark of Amazon Technologies, Inc.
In 1991, the National Science Foundation, which governed how the Internet was used, lifted restrictions on its commercial use. The year 1994 saw the establishment of both eBay and Amazon.com, two true pioneers in the use of the new digital marketplace. A mad rush of investment in Internet-based businesses led to the dot-com boom through the late 1990s, and then the dot-com bust in 2000. While much can be learned from the speculation and crazy economic theories espoused during that bubble, one important outcome for businesses was that thousands of miles of Internet connections were laid around the world during that time. The world became truly “wired” heading into the new millenium, ushering in the era of globalization, which we will discuss in chapter 11.
As it became more expected for companies to be connected to the Internet, the digital world also became a more dangerous place. Computer viruses and worms, once slowly propagated through the sharing of computer disks, could now grow with tremendous speed via the Internet. Software written for a disconnected world found it very difficult to defend against these sorts of threats. A whole new industry of computer and Internet security arose. We will study information security in chapter 6.
Web 2.0
As the world recovered from the dot-com bust, the use of technology in business continued to evolve at a frantic pace. Websites became interactive; instead of just visiting a site to find out about a business and purchase its products, customers wanted to be able to customize their experience and interact with the business. This new type of interactive website, where you did not have to know how to create a web page or do any programming in order to put information online, became known as web 2.0. Web 2.0 is exemplified by blogging, social networking, and interactive comments being available on many websites.  Some industries, such as bookstores, found themselves relegated to a niche status. Others, such as video rental chains and travel agencies, simply began going out of business as they were replaced by online technologies. This process of technology replacing a middleman in a transaction is called disintermediation.
As the world became more connected, new questions arose. Should access to the Internet be considered a right? Can I copy a song that I downloaded from the Internet? How can I keep information that I have put on a website private? What information is acceptable to collect from children? Technology moved so fast that policymakers did not have enough time to enact appropriate laws, making for a Wild West–type atmosphere. Ethical issues surrounding information systems will be covered in chapter 12.
The Post-PC World
After thirty years as the primary computing device used in most businesses, sales of the PC are now beginning to decline as sales of tablets and smartphones are taking off. Just as the mainframe before it, the PC will continue to play a key role in business, but will no longer be the primary way that people interact and do business. The limited storage and processing power of these devices is being offset by a move to “cloud” computing, which allows for storage, sharing, and backup of information on a massive scale. This will require new rounds of thinking and innovation on the part of businesses as technology continues to advance.
| Era | Hardware | Operating System | Applications |
|---|---|---|---|
|
Mainframe
(1970s) |
Terminals connected to mainframe computer. |
Time-sharing
(TSO) on MVS |
Custom-written
MRP software |
|
PC
(mid-1980s) |
IBM PC or compatible. Sometimes connected to mainframe computer via
expansion card. |
MS-DOS |
WordPerfect,
Lotus 1-2-3 |
|
Client-Server
(late 80s to early 90s) |
IBM PC “clone” on a Novell Network. | Windows for Workgroups |
Microsoft
Word, Microsoft Excel |
|
World
Wide Web (mid-90s to early 2000s) |
IBM PC “clone” connected to company intranet. | Windows XP |
Microsoft
Office, Internet Explorer |
| Web 2.0 (mid-2000s to present) | Laptop connected to company Wi-Fi. | Windows 7 |
Microsoft
Office, Firefox |
|
Post-PC
(today and beyond) |
Apple iPad | iOS |
Mobile-friendly
websites, mobile apps |


7.4: Multiple Globalizations
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- Petr Szczepanik
- University of California Press
We should avoid the pitfall of misrepresenting knowledge transfer (and spillover) enabled by spatial proximity, interaction, and monitoring as entirely positive or innocent. Contrary to some journalistic accounts, it doesn’t come as an automatic, mechanistic, and unidirectional process. 27 Rather, it is important to recognize that effective knowledge absorption happens only when locals develop their own capabilities, that learning is usually a mutual process, even though it may be perceived in negative terms due to the adverse effects it is seen to have on the local culture. We might also recognize that unlearning can be just as important as learning, especially in a postsocialist working environment. Most of my Czech interview subjects talked about learning. An analysis of their revelations allows us to identify four potential paths of globalizing knowledge transfer as well as the barriers to such a transfer. These are centered respectively on incoming producers, production service providers, local independent producers, and the regional strategy of a multinational corporation (where offshoring and direct foreign investment can transform local production norms and practices). Given the limited scope of this chapter, I will restrict my focus to cases in which significant face-to-face interaction took place between Czech and overseas personnel. Before doing so, however, I offer a brief overview of local production practice and its limitations.
Czech film production is strongly influenced by a small, fragmented marketplace, television aesthetics, and the public broadcaster’s long-standing position as the country’s leading producer-distributor of indigenous feature films and documentaries over the last twenty years. In this period, Czech cinema held a strong market share of up to 30 percent; however, this has started to drop as newly digitized theaters express a preference for Hollywood fare. Czech films rely on location shooting, contemporary topics or nostalgia for the country’s recent state-socialist past, and a bittersweet tone, and they are squarely aimed at families. Many of these low-budget films are considered part of the mainstream locally but travel badly. What is more, bigger-budget films and art-house pictures both tend to fare poorly at the international box office or on the festival circuit, even by the modest standards of other East-Central European nations, such as Hungary and Poland. Czech television programs have also struggled internationally, not least because broadcasters have been reticent to alienate their prime mature, conservative domestic audience with unsettling subject matter or radical aesthetics.
Outside observers and policymakers concluded that knowledge transfer would lead incoming producers to gradually transform the practices and styles of the domestic industry. Such a change would come from sharing a labor pool and infrastructure, and from interaction, observation, and imitation. This being said, overseas producers appear to have little interest in reshaping local production—by, for example, hiring local above-the-line talent or hiring Czechs as department heads. In short, there is no clear evidence of any transformation resulting from their presence. Even the BBC—which practices runaway production via its international branches, BBC Worldwide and BBC America—has not promoted its public service ethics or aesthetics during production. As the experience of Czech crews working on The Musketeers (2014–) suggests, the presence of the BBC is felt in its division of British and Czech workers and its safety regulations. Czech personnel did not even recognize the corporation as the producer of this series, noting no significant differences between working on a BBC venture or other Anglo-American projects. 28
Second, it was anticipated that service providers would eventually diversify into producing Czech-language films. However, despite their claims to the contrary, none of the production service heavyweights—Stillking, Czech Anglo Productions, and Etic Films—has branched out into original feature productions. One of the few exceptions is the former Lucasfilm producer Rick McCallum, whose company Film United provides production services for projects like Canal+’s series Borgia (2011–), while developing its own fully local and coproduced projects, such as a story of Czech anticommunist resistance fighters, So Far So Good (in development). It remains to be seen whether Film United can support high-end Czech genre products.
More typical is the approach of Stillking, a company with solid knowledge of the Czech filmmaking community but evidently little interest in producing or coproducing Czech films. Minkowski, its production head, has met numerous Czech producers but never found a reason to work with them: “We know them and they know us, . . . but we just didn’t find something that makes sense. I don’t think we are the first stop for them to come and produce Czech movies, because we are not really Czech producers.” He admits that the number of American films shot in Prague did not increase the importance of Czech films because “there is no connection there.” 29 On the other hand, Minkowski claims that Stillking trains local crews who can then improve the technical quality of the local product. However, this claim relates only to certain aspects of the production process—primarily art direction, special and visual effects, stunts, and to a lesser extent, makeup, costumes, and camera operation. Stillking-affiliated production managers usually do not work on Czech productions, and Czech above-the-line talent does not work for Stillking.
The rate at which Czech personnel enjoy professional upward mobility within transnational crews differs from case to case, partially determined by the nationality, size, and organizational structure of the coproducer. The smaller and more flexible the company, the more Czechs hold positions close to first-line decision makers, and vice versa. Specializing in bigger-budget projects, Stillking employs a large workforce but typically only one Czech head of department (in production design). In these large crews with their military-like organization, locals usually work under second-line decision makers while operating in a segregated labor sphere. They are largely unaware of the creative effects of their roles. According to Minkowski, this type of segregation is typical of Barrandov’s costume department, where a staff of mainly non-English-speaking women operates in a socially and spatially isolated workspace. 30
Local independent producers represent a third potential path for globalizing knowledge transfer. They work on wholly Czech projects, coproductions, and minority coproductions with European partners, and some provide production services. Often independent producers specialize in partnerships with given countries or regions, as was the case with the Indian film Rockstar (2011). 31 Irregular, limited to practical services and dependent on narrow networks of contacts, such collaborations do not induce long-lasting knowledge transfers that would affect the quality of local products.
A fourth pathway involves a multinational corporation operating on the local market. In 1991, HBO Europe established central offices in the Hungarian capital of Budapest. Soon after, it set up an additional fourteen branches across Europe, all but one in postsocialist countries. Four of these—Budapest, Prague, Warsaw, and Bucharest—opened an original programming department. These were responsible for providing culturally local quality content for the company’s subscription television and HBO GO online services, thus emulating its approach to the U.S. market. 32 A new two-tiered production strategy has come to the fore since HBO Europe recruited the experienced producer Antony Root as its new executive vice president for original programming and production. On the one hand, the company broadcasts low-budget licensed series to test local responses to a property. For instance, it produced adaptations of two Israeli series, In Treatment and When Shall We Kiss , helmed by renowned local directors and featuring established actors, for each of the four national markets noted above. On the other hand, it produces big-budget event miniseries, which, in Root’s words, “put a stake in the ground for a certain kind of quality and values in a show and differentiate ourselves [sic] in the market.” 33 One example of this approach is The Burning Bush (2013), an award-winning three-part drama about the Czech national hero and martyr Jan Palach, who immolated himself to protest the 1968 Soviet occupation of the country.
The screenplay for The Burning Bush was rejected by the Czech public service broadcaster before being acquired by HBO. The series was directed by Polish FAMU graduate Agnieszka Holland, who had previously worked for HBO in the United States. It was written by then-unknown Czech screenwriter Štěpán Hulík, and coproduced by newcomer Tomáš Hrubý. When The Burning Bush received fourteen awards from the national film academy after being released as a theatrical feature, it was apparent that a new approach, based on HBO’s meticulous development process, was emerging. 34 As the company’s Budapest-based head of development suggested, HBO’s gradual development of local talent and adaptation of American-style project development practices were crucial albeit challenging steps to striking a good balance between maintaining the cultural specificities of local fare and increasing its general quality. 35 The success of The Burning Bush generated intense buzz across the Czech production sector, nowhere more than among public service television producers. Embarrassed about passing up this project, they singled out The Burning Bush as a new benchmark to which their own quality serial drama ought to aspire.


27.6: Sample proposal (Measuring g using a pendulum)
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Summary and Goal
One can measure the gravitational constant, \(g\) , by measuring the period of a pendulum of a known length, requiring only a string, mass, ruler and timer. Because the experimental design can be easily adjusted and the experiment is simple, the experiment has a high chance of success.
Method and equipment
The period of a pendulum of length \(L\) is easily shown to be given by:
\[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]
Thus, by measuring the period, \(T\) , of a pendulum as well as its length, one can determine the value of \(g\) :
\[\begin{aligned} g=\frac{4\pi^{2}L}{T^{2}}\end{aligned}\]
One can carry out the experiment using the following materials:
- a mass
- inextensible string
- a meter stick
- stand to attach string
- cell-phone with timer and slow-motion camera
The materials listed above are all inexpensive and can be easily obtained. It is recommended that the experiment be completed indoors at room temperature, in order to minimize any environmental effects.
One should tie the string to the mass at one end and the stand at the other, and measure the length, \(L\) , of the string from the point on the stand to the center of mass of the mass.
The period of the pendulum is measured by timing how long it takes the pendulum to complete 20 oscillations and dividing that time by 20. This will be more precise than trying to time the period of a single oscillation.
The pendulum should be released from \(90^{\circ}\) . When releasing the pendulum, the string should be pulled taught, and the team member’s eye that is measuring the angle should be situated parallel to the measuring device.
A slow-motion video will be taken of the pendulum to track the time of the oscillation in order to minimize error due to reaction time. The team member in charge of taking the video will start the video shortly before the pendulum is released. After releasing the pendulum, the team should record 20 oscillations before stopping the pendulum and the video. Data from the video should be entered into a Jupyter Notebook. It is recommended that this measurement be repeated at least 5 times.
The uncertainty in the time should be taken as half of the smallest division of the cell-phone timer, and the uncertainty in the length of the pendulum as half the smallest division of the meter stick used to measure the length of the pendulum.
Foreseeable issues in this experiment may arise when trying to find a string that is optimally inextensible, as any extensibility will cause error in the results. Additionally, being able to measure exactly 90 as the drop-angle for the pendulum could be difficult. In order to correct for this, the team member who is dropping the pendulum must stand directly parallel to the measuring device, minimizing parallax error.
The measure of success will be determined by the uncertainty and precision of the measured value of \(g\) . If the measured value of \(g\) has a relative uncertainty that is less than 10 %, and is consistent with the accepted value, then one can consider the experiment to have been carried out successfully.
Team and timeline
One should be able to complete the experiment and analysis in approximately 1 hour and 30 minutes with the data being collected in the first 30 minutes. The remainder of the time should be spent processing the data and writing the experimental report. Following the strengths of the members of the team, the following people should be responsible for leading the following tasks, while everyone participates:
- Alice: building the pendulum
- Brice: taking the measurements
- Chloë: analyzing the data
- Dennis: writing and formatting


6.13: The Massive Atmosphere of Venus
Learning Objectives
By the end of this section, you will be able to:
- Describe the general composition and structure of the atmosphere on Venus
- Explain how the greenhouse effect has led to high temperatures on Venus
The thick atmosphere of Venus produces the high surface temperature and shrouds the surface in a perpetual red twilight. Sunlight does not penetrate directly through the heavy clouds, but the surface is fairly well lit by diffuse light (about the same as the light on Earth under a heavy overcast). The weather at the bottom of this deep atmosphere remains perpetually hot and dry, with calm winds. Because of the heavy blanket of clouds and atmosphere, one spot on the surface of Venus is similar to any other as far as weather is concerned.
Composition and Structure of the Atmosphere
The most abundant gas on Venus is carbon dioxide (\(CO_2\)), which accounts for 96% of the atmosphere. The second most common gas is nitrogen. The predominance of carbon dioxide over nitrogen is not surprising when you recall that Earth’s atmosphere would also be mostly carbon dioxide if this gas were not locked up in marine sediments (see the discussion of Earth’s atmosphere in Earth as a Planet).
Table \(\PageIndex{1}\) compares the compositions of the atmospheres of Venus, Mars, and Earth. Expressed in this way, as percentages, the proportions of the major gases are very similar for Venus and Mars, but in total quantity, their atmospheres are dramatically different. With its surface pressure of 90 bars, the venusian atmosphere is more than 10,000 times more massive than its martian counterpart. Overall, the atmosphere of Venus is very dry; the absence of water is one of the important ways that Venus differs from Earth.
| Table \(\PageIndex{1}\): Atmospheric Composition of Earth, Venus, and Mars | |||
|---|---|---|---|
| Gas | Earth | Venus | Mars |
| Carbon dioxide (CO 2 ) | 0.03% | 96% | 95.3% |
| Nitrogen (N 2 ) | 78.1% | 3.5% | 2.7% |
| Argon (Ar) | 0.93% | 0.006% | 1.6% |
| Oxygen (O 2 ) | 21.0% | 0.003% | 0.15% |
| Neon (Ne) | 0.002% | 0.001% | 0.0003% |
The atmosphere of Venus has a huge troposphere (region of convection) that extends up to at least 50 kilometers above the surface (Figure \(\PageIndex{1}\)). Within the troposphere, the gas is heated from below and circulates slowly, rising near the equator and descending over the poles. Being at the base of the atmosphere of Venus is something like being a kilometer or more below the ocean surface on Earth. There, the mass of water evens out temperature variations and results in a uniform environment—the same effect the thick atmosphere has on Venus.
In the upper troposphere, between 30 and 60 kilometers above the surface, a thick cloud layer is composed primarily of sulfuric acid droplets. Sulfuric acid \(H_2SO_4\)) is formed from the chemical combination of sulfur dioxide (\(SO_2\)) and water (\(H_2O\)). In the atmosphere of Earth, sulfur dioxide is one of the primary gases emitted by volcanoes, but it is quickly diluted and washed out by rainfall. In the dry atmosphere of Venus, this unpleasant substance is apparently stable. Below 30 kilometers, the Venus atmosphere is clear of clouds.
Surface Temperature on Venus
The high surface temperature of Venus was discovered by radio astronomers in the late 1950s and confirmed by the Mariner and Venera probes. How can our neighbor planet be so hot? Although Venus is somewhat closer to the Sun than is Earth, its surface is hundreds of degrees hotter than you would expect from the extra sunlight it receives. Scientists wondered what could be heating the surface of Venus to a temperature above 700 K. The answer turned out to be the greenhouse effect .
The greenhouse effect works on Venus just as it does on Earth, but since Venus has so much more \(CO_2\)—almost a million times more—the effect is much stronger. The thick \(CO_2\) acts as a blanket, making it very difficult for the infrared (heat) radiation from the ground to get back into space. As a result, the surface heats up. The energy balance is only restored when the planet is radiating as much energy as it receives from the Sun, but this can happen only when the temperature of the lower atmosphere is very high. One way of thinking of greenhouse heating is that it must raise the surface temperature of Venus until this energy balance is achieved.
Has Venus always had such a massive atmosphere and high surface temperature, or might it have evolved to such conditions from a climate that was once more nearly earthlike? The answer to this question is of particular interest to us as we look at the increasing levels of \(CO_2\) in Earth’s atmosphere. As the greenhouse effect becomes stronger on Earth, are we in any danger of transforming our own planet into a hellish place like Venus?
Let us try to reconstruct the possible evolution of Venus from an earthlike beginning to its present state. Venus may once have had a climate similar to that of Earth, with moderate temperatures, water oceans, and much of its \(CO_2\) dissolved in the ocean or chemically combined with the surface rocks. Then we allow for modest additional heating—by gradual increase in the energy output of the Sun, for example. When we calculate how Venus’ atmosphere would respond to such effects, it turns out that even a small amount of extra heat can lead to increased evaporation of water from the oceans and the release of gas from surface rocks.
This in turn means a further increase in the atmospheric \(CO_2\) and \(H_2O\), gases that would amplify the greenhouse effect in Venus’ atmosphere. That would lead to still more heat near Venus’ surface and the release of further \(CO_2\) and \(H_2O\). Unless some other processes intervene, the temperature thus continues to rise. Such a situation is called the runaway greenhouse effect .
We want to emphasize that the runaway greenhouse effect is not just a large greenhouse effect; it is an evolutionary process . The atmosphere evolves from having a small greenhouse effect, such as on Earth, to a situation where greenhouse warming is a major factor, as we see today on Venus. Once the large greenhouse conditions develop, the planet establishes a new, much hotter equilibrium near its surface.
Reversing the situation is difficult because of the role water plays. On Earth, most of the \(CO_2\) is either chemically bound in the rocks of our crust or dissolved by the water in our oceans. As Venus got hotter and hotter, its oceans evaporated, eliminating that safety valve. But the water vapor in the planet’s atmosphere will not last forever in the presence of ultraviolet light from the Sun. The light element hydrogen can escape from the atmosphere, leaving the oxygen behind to combine chemically with surface rock. The loss of water is therefore an irreversible process: once the water is gone, it cannot be restored. There is evidence that this is just what happened to the water once present on Venus.
We don’t know if the same runaway greenhouse effect could one day happen on Earth. Although we are uncertain about the point at which a stable greenhouse effect breaks down and turns into a runaway greenhouse effect, Venus stands as clear testament to the fact that a planet cannot continue heating indefinitely without a major change in its oceans and atmosphere. It is a conclusion that we and our descendants will surely want to pay close attention to.
Summary
The atmosphere of Venus is 96% \(CO_2\). Thick clouds at altitudes of 30 to 60 kilometers are made of sulfuric acid, and a \(CO_2\), which is greenhouse effect maintains the high surface temperature. Venus presumably reached its current state from more earthlike initial conditions as a result of a runaway greenhouse effect, which included the loss of large quantities of water.
Glossary
- runaway greenhouse effect
- the process by which the greenhouse effect, rather than remaining stable or being lessened through intervention, continues to grow at an increasing rate
Contributors and Attributions
-
Andrew Fraknoi (Foothill College), David Morrison (NASA Ames Research Center), Sidney C. Wolff (National Optical Astronomy Observatory) with many contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/astronomy ).


3: Orbits and Gravity
How would you find a new planet at the outskirts of our solar system that is too dim to be seen with the unaided eye and is so far away that it moves very slowly among the stars? This was the problem confronting astronomers during the nineteenth century as they tried to pin down a full inventory of our solar system.
If we could look down on the solar system from somewhere out in space, interpreting planetary motions would be much simpler. But the fact is, we must observe the positions of all the other planets from our own moving planet. Scientists of the Renaissance did not know the details of Earth’s motions any better than the motions of the other planets. Their problem, as we saw in Observing the Sky: The Birth of Astronomy, was that they had to deduce the nature of all planetary motion using only their earthbound observations of the other planets’ positions in the sky. To solve this complex problem more fully, better observations and better models of the planetary system were needed.
-
- 3.1: The Laws of Planetary Motion
- Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion. Kepler’s laws describe the behavior of planets in their orbits as follows: (1) planetary orbits are ellipses with the Sun at one focus; (2) in equal intervals, a planet’s orbit sweeps out equal areas; and (3) the relationship between the orbital period (P) and the semimajor axis (a) of an orbit is given by \(P^2 = a^3\) (when a is in units
-
- 3.2: Newton’s Great Synthesis
- In his Principia, Isaac Newton established the three laws that govern the motion of objects: (1) objects continue to be at rest or move with a constant velocity unless acted upon by an outside force; (2) an outside force causes an acceleration (and changes the momentum) for an object; and (3) for every action there is an equal and opposite reaction. Momentum is a measure of the motion of an object and depends on both its mass and its velocity.
-
- 3.3: Newton’s Universal Law of Gravitation
- Gravity, the attractive force between all masses, is what keeps the planets in orbit. Newton’s universal law of gravitation relates the gravitational force to mass and distance. The force of gravity is what gives us our sense of weight. Unlike mass, which is constant, weight can vary depending on the force of gravity (or acceleration) you feel. When Kepler’s laws are reexamined in the light of Newton’s gravitational law, it becomes clear that the masses of both objects are important for the thir
-
- 3.4: Orbits in the Solar System
- The closest point in a satellite orbit around Earth is its perigee, and the farthest point is its apogee (corresponding to perihelion and aphelion for an orbit around the Sun). The planets follow orbits around the Sun that are nearly circular and in the same plane. Most asteroids are found between Mars and Jupiter in the asteroid belt, whereas comets generally follow orbits of high eccentricity.
-
- 3.5: Motions of Satellites and Spacecraft
- The orbit of an artificial satellite depends on the circumstances of its launch. The circular satellite velocity needed to orbit Earth’s surface is 8 kilometers per second, and the escape speed from our planet is 11 kilometers per second. There are many possible interplanetary trajectories, including those that use gravity-assisted flybys of one object to redirect the spacecraft toward its next target.
-
- 3.6: Gravity with More Than Two Bodies
- Calculating the gravitational interaction of more than two objects is complicated and requires large computers. If one object (like the Sun in our solar system) dominates gravitationally, it is possible to calculate the effects of a second object in terms of small perturbations. This approach was used by John Couch Adams and Urbain Le Verrier to predict the position of Neptune from its perturbations of the orbit of Uranus and thus discover a new planet mathematically.
Thumbnail: This space habitat and laboratory orbits Earth once every 90 minutes. (credit: modification of work by NASA)


26.1: Introduction
Chapter Objectives
After studying this chapter, you will be able to:
- Identify the body’s main fluid compartments
- Define plasma osmolality and identify two ways in which plasma osmolality is maintained
- Identify the six ions most important to the function of the body
- Define buffer and discuss the role of buffers in the body
- Explain why bicarbonate must be conserved rather than reabsorbed in the kidney
- Identify the normal range of blood pH and name the conditions where one has a blood pH that is either too high or too low
Homeostasis, or the maintenance of constant conditions in the body, is a fundamental property of all living things. In the human body, the substances that participate in chemical reactions must remain within narrows ranges of concentration. Too much or too little of a single substance can disrupt your bodily functions. Because metabolism relies on reactions that are all interconnected, any disruption might affect multiple organs or even organ systems. Water is the most ubiquitous substance in the chemical reactions of life. The interactions of various aqueous solutions—solutions in which water is the solvent—are continuously monitored and adjusted by a large suite of interconnected feedback systems in your body. Understanding the ways in which the body maintains these critical balances is key to understanding good health.